This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A334860 #24 Jun 11 2020 23:43:40
%S A334860 1,2,3,4,6,9,8,16,5,36,18,81,12,64,32,256,10,25,72,1296,27,324,162,
%T A334860 6561,24,144,128,4096,48,1024,512,65536,15,100,50,625,108,5184,2592,
%U A334860 1679616,54,729,648,104976,243,26244,13122,43046721,20,576,288,20736,192,16384,8192,16777216,96,2304,2048,1048576,768,262144,131072,4294967296,30
%N A334860 a(0) = 1, a(1) = 2, after which, a(2n) = A334747(a(n)), a(2n+1) = a(n)^2.
%C A334860 This irregular table can be represented as a binary tree. Each child to the left is obtained by applying A334747 to the parent, and each child to the right is obtained by squaring the parent:
%C A334860 1
%C A334860 |
%C A334860 ...................2...................
%C A334860 3 4
%C A334860 6......../ \........9 8......../ \........16
%C A334860 / \ / \ / \ / \
%C A334860 / \ / \ / \ / \
%C A334860 / \ / \ / \ / \
%C A334860 5 36 18 81 12 64 32 256
%C A334860 10 25 72 1296 27 324 162 6561 24 144 128 4096 48 1024 512 65536
%C A334860 etc.
%C A334860 This is the mirror image of the tree in A334866.
%C A334860 Fermi-Dirac primes, A050376, occur at rightward growing branches that originate from primes situated at the left edge.
%C A334860 The tree illustrated in A163511 is expanded as x -> 2*x for the left child and x -> A003961(x) for the right child, while this tree is expanded as x -> A225546(2*A225546(x)) for the left child, and x -> A225546(A003961(A225546(x))) for the right child.
%H A334860 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A334860 a(0) = 1, a(1) = 2; and for n > 0, a(2n) = A334747(a(n)), a(2n+1) = a(n)^2.
%F A334860 a(n) = A225546(A163511(n)).
%F A334860 For n >= 0, a(2^n) = A019565(1+n), a(2^((2^n)-1)) = A000040(1+n).
%F A334860 A334109(a(n)) = A334204(n).
%F A334860 It seems that for n >= 1, A048675(a(n)) = A135529(n) = A048675(A163511(n)).
%o A334860 (PARI)
%o A334860 A334747(n) = { my(c=core(n), m=n); forprime(p=2, , if(c % p, m*=p; break, m/=p)); m; }; \\ From A334747
%o A334860 A334860(n) = if(n<=1,1+n,if(!(n%2),A334747(A334860(n/2)),A334860((n-1)/2)^2));
%Y A334860 Cf. A000290, A225546, A334204, A334747, A334859 (inverse), A334866 (mirror image).
%Y A334860 Cf. A001146 (right edge of the tree), A019565 (left edge), A334110 (the right children of the left edge).
%Y A334860 Composition of permutations A163511 and A225546.
%K A334860 nonn,tabf
%O A334860 0,2
%A A334860 _Antti Karttunen_, Jun 08 2020